Using the overlap representation of the LCWFs, the sea quarks Sivers function can be calculated from the following expression [1]}, [2]}
\( &\frac{2(\widehat{s}_T\times k_T)\cdot \widehat{P}}{M}f_{1T}^\bot (x,y,k_T^2,r_T^2)=\int \frac{d^2r^{\prime }_T}{16\pi ^3}G(x,k_T,k^{\prime }_T)\nonumber \\&\sum _{\lbrace \lambda \rbrace }[\psi ^{\uparrow *}_{{\lambda _B}{\lambda _q}{\lambda _{\bar{q}}}}(x,y,k_T,r_T)\psi ^{\uparrow }_{{\lambda _B}{\lambda _q}{\lambda _{\bar{q}}}}(x,y,k_T,r^{\prime }_T)\nonumber \\&-\psi ^{\downarrow *}_{{\lambda _B}{\lambda _q}{\lambda _{\bar{q}}}}(x,y,k_T,r_T)\psi ^{\downarrow }_{{\lambda _B}{\lambda _q}{\lambda _{\bar{q}}}}(x,y,k_T,r^{\prime }_T)] \) 
